You keep your coffee in a sealable thermal mug which has thermal conductivity k-

ID: 2123005 • Letter: Y

Question

You keep your coffee in a sealable thermal mug which has thermal conductivity k-0.036 W/m k. The

mug is about 15 cm high and its average radius is about 3.0 cm and has wall thickness of 5.0 mm. The

coffee can be considered to have the same properties of water. If the mug is filled with coffee and placed

in room temperature (25 C), Starting from boiling temperature, how long (in minutes) will it take the

coffee to cool down to: (a) 75 C, (b) 50 C, and (c) 30 C?

**Answer all parts and show work for five star rating!!!

mass of coffee=volume*density=0.15*0.03*0.005*1000=0.0225 kg

using newton's law of cooling,

dT/dt=-k*(T-25)

dT/(T-25)=-k*dt

ln(T-25)=-k*t+C

at t=0,

T=100

so we get c=ln(75)

complete equation:

ln(T-25)=-0.036*t+ln(75)

putting the values,

a)time taken=11.26 sec

b)time taken =30.517 sec

c)time taken=75.22 sec

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